Collective transport in random media: from superconductors to earthquakes

In these lectures, a variety of non-equilibrium transport phenomena are introduced that all involve, in some way, elastic manifolds being driven through random media. A simple class of models is studied focussing on the behavior near to the critical "depinning" force above which persistent motion occurs in these systems. A simple mean field theory and a "toy" model of "avalanche" processes are analyzed and used to motivate the general scaling picture found in recent renormalization group studies. The general ideas and results are then applied to various systems: sliding charge density waves; critical current behavior of vortices in superconductors, dynamics of cracks, and simple models of a geological fault. The roles of thermal fluctuations, defects, inertia? and elastic wave propagation are all discussed briefly. (C) 1998 Elsevier Science B.V. All rights reserved.